Theory of intracavity optical second-harmonic generation

An analysis of optical second-harmonic generation internal to the laser cavity is presented. It is shown that the maximum second-harmonic power generated in this way is equal to the maximum fundamental power available from the laser. Further, it is found that there exists a value of nonlinearity that optimally couples the harmonic out for all power levels of the laser. The magnitude of the nonlinearity required for optimum coupling is shown to be proportional to the linear losses at the fundamental and inversely proportional to the saturation parameter for the laser transition. For the YAlG:Nd laser at 1.06 μ using Ba
2
NaNb
5
O
15
as the nonlinear material, the required crystal length for optimum coupling is given by
l\min{c}\max{2}(cm)\simeq 2.7 \times 10^{2}L/f
where
L
is the linear round-trip loss and
f
is the ratio of the fundamental power density in the nonlinear crystal to that in the laser medium. For low-loss cavities, optimum coupling can thus be achieved for crystal lengths of 1 cm or less. The use of a mirror or mirrors within the cavity, reflecting at the harmonic, is considered as a means to couple out the total harmonic in one direction. Considerations of temperature stability and the finite oscillating linewidth of the laser are shown to favor a configuration with a single harmonic mirror located on the same surface as the fundamental mirror.